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Will computers make mathematicians obsolete? 
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#19
Nov812, 01:43 AM

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NO! Computers will never make mathematicians obsolete. This is a major point made in the movie, 2001: A Space Odyssey.



#20
Nov812, 02:28 AM

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Don't worry about if it'll be useless or not just do what you love. In this current age nobody can really tell you accurately what jobs you might be able to find 510 years down the road or what skills it'll take to get the job.



#21
Nov812, 02:01 PM

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I was about to say that computers will never replace mathematicians, but I'll hold back so as not to risk displeasing our future, robot overlords.



#22
Nov812, 02:23 PM

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"What a computer might possibly do is to randomly come up with theorems. So you start with axioms, and you apply the logical rules on that to come up with new true statements. Given enough time, the compute might (or not) come up with a proof for mathematical statements. But the numbers involved are extremely large here and I don't see this happening any time soon." So wouldn't that kind of computers at least replace mathematicians in creating new theorems? 


#23
Nov812, 02:29 PM

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Computers will make mathematicians who cannot use computers obsolete.
Computers make less demand for researchers to know mathematics... but only because of mathematicians writing computer programs. 


#24
Nov812, 02:35 PM

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#25
Nov812, 02:42 PM

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I didn't say mathematician. I'm talking about science research (including biology). I never learned the Adams mueller bashforth method (or whatever) but I can still solve differential equations using it.
I'm saying mathematicians supply us the benefits from computers so they won't be obsolete. 


#26
Nov812, 03:46 PM

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If you didn't even know it was possible that a finite difference approximation to a DE has completely different solutions from the underlying DE, maybe you need to learn some more math before you outsource everything to a computer. 


#27
Nov812, 08:18 PM

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I knew that... and I had to write my own fourth order rungekutta method before being turned loose with a computer in the first place.
But... I didn't have to write my own adams moulton bashform predictorcorrector to use it. I've never even studied predictorcorrectors. I've actually had problems with them though... the interpolation step acts like a perturbation which sensitive systems can't handle, so I can actually get nondeterministic results with the predictorcorrector method, depending on where interpolation is interrupted by my conditions detector. They just don't work with systems that have a positive Lyapunov exponent. In this case, I had to go back to rungekutta, as there's a fixed step option with it. Anyway, I wouldn't mention any of this in my publication, so you wouldn't know it. I verify the system with common sense and by verifying that it behaves correctly in alreadydetermined parameter regimes. 


#28
Nov1312, 11:26 AM

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#29
Nov1312, 11:32 AM

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That said, there have been programs which have been able to find good conjectures and proof them. I'll search for a link, but I remember that some people programmed a computer to find conjectures in number theory and the computer came up with the fundamental theorem of arithmetic (any nonzero, noninvertible number can be expressed in an essantially unique way as the product of prime numbers). I don't remember if the program was able to prove it, but it's a nice feat nevertheless. But of course, modern mathematics is faaaaar more advanced than simple theorems like that. 


#30
Nov1512, 12:22 PM

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Could a computer replace Newton and come up with calculus? Probably not.



#31
Nov1512, 12:43 PM

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There is already a sizable branch of mathematics close to computer sciences that deals with developing algorithms for computers so that they can carry out math.
The more powerful the computers, the wider the scope for exotic math to be carried out by them, so if anything, the progress in computers has increased the need for mathematicians. As to the mind being just another machine that can be replaced by a computer  this probably is true in theory, but we are still a far cry away from that. "Artificial intelligence" can so far only solve very few, very very well defined problems. Last time I checked, you could not tell a computer "sit in that car, learn to drive, drive yourself to that Chess tournament, learn the game, win, come back and do my homework on partial differential equations". PS: I did not want to give the impression that I could do that :) 


#32
Nov1512, 10:08 PM

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That's the theory, but no one knows how to do it. So one may or may not believe that. 


#33
Nov1512, 10:13 PM

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The most positive results were Doug Lenat's from CMU. It so happens that I worked for a former CMU professor who told me that the consensus there was that Lenat's results were bogus. The basic problem is that mathematicians do not know how they prove difficult theorems. Brute force search, such as used in chess, seems entirely unfeasible even in theory. So I gave up on that. 


#34
Nov1612, 01:42 AM

P: 390

To OP: No. We have programs which simulate physics very accurately. But it did not make physicists obsolete.



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